Chapter 6, Problem 19RE

To determine

To evaluate the given integral.

Answer to Problem 19RE

  ${\displaystyle \underset{0}{\overset{1}{\int }}\left(8s^3-12s^2+5\right)ds}=3$

Explanation of Solution

Given:

  ${\displaystyle \underset{0}{\overset{1}{\int }}\left(8s^3-12s^2+5\right)ds}$

Calculation:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{1}{\int }}\left(8s^3-12s^2+5\right)ds}={\left[8\cdot \frac{s^4}{4}-12\cdot \frac{s^3}{3}+5s\right]}_0^1\\ ={\left[2s^4-4s^3+5s\right]}_0^1\\ =\left[2{\left(1\right)}^4-4{\left(1\right)}^3+5\left(1\right)\right]-\left[2{\left(0\right)}^4-4{\left(0\right)}^3+5\left(0\right)\right]\\ =2-4+5\\ =3\end{array}$